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Critical values for cointegration tests
 Eds.), LongRun Economic Relationship: Readings in Cointegration
, 1991
"... This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means of ..."
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Cited by 506 (3 self)
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This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means of response surface regressions in which critical values depend on the sample size. From these regressions, asymptotic critical values can be read off directly, and critical values for any finite sample size can easily be computed with a hand calculator. Added in 2010 version: A new appendix contains additional results that are more accurate and cover more cases than the ones in the original paper.
Testing and modeling multivariate threshold models
 Journal of the American Statistical Association
, 1998
"... Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this paper, we use predictive residuals to construct a test statistic to detect threshold nonlinearity in a vector time series and propose a procedure for ..."
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Cited by 99 (0 self)
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Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this paper, we use predictive residuals to construct a test statistic to detect threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The nitesample performance of the proposed test is studied by simulation. The modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the costofcarrying the contracts. In this particular application, thresholds are determined in part by the transaction costs. We also apply the proposed procedure to U.S. monthly interest rates and two river ow series of Iceland.
Elements of Forecasting
"... Most good texts arise from the desire to leave one's stamp on a discipline by training future generations of students, coupled with the recognition that existing texts are inadequate in various respects. My motivation is no different. There is a real need for a concise and modern introductory f ..."
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Cited by 88 (4 self)
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Most good texts arise from the desire to leave one's stamp on a discipline by training future generations of students, coupled with the recognition that existing texts are inadequate in various respects. My motivation is no different. There is a real need for a concise and modern introductory forecasting text. A number of features distinguish this book. First, although it uses only elementary mathematics, it conveys a strong feel for the important advances made since the work of Box and Jenkins more than thirty years ago. In addition to standard models of trend, seasonality, and cycles, it touches – sometimes extensively – upon topics such as: data mining and insample overfitting statistical graphics and exploratory data analysis model selection criteria recursive techniques for diagnosing structural change nonlinear models, including neural networks regimeswitching models unit roots and stochastic trends
Does the law of one price really hold for commodity prices
 American Journal of Agricultural Economics
, 1989
"... In spite ofthe empirical failure ofthe "Law of One Price, " it is usually assumed that commodity prices are perfectly arbitraged, at least in the long run. This paper argues that this assumption is counterfactual and that much of the empirical evidence provided to support it is flawed and ..."
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Cited by 86 (0 self)
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In spite ofthe empirical failure ofthe "Law of One Price, " it is usually assumed that commodity prices are perfectly arbitraged, at least in the long run. This paper argues that this assumption is counterfactual and that much of the empirical evidence provided to support it is flawed and affected by econometric shortcomings (spurious regressions, nonstationarity in the data, inappropriate use of first differences). An alternative methodology (cointegration), by which a longrun relationship between nonstationary series can be tested, is proposed. Tests of nonstationarity and cointegration for a group of commodities show quite uniformly that the "Law of One Price, " as a longrun relationship, fails, and that deviations from the pattern are permanent. Key words: cointegration tests, commodity prices, law of one price, spurious regressions. unitroot tests. According to several models of exchange rate determination, commodity price arbitrage, at least for some goods, is a necessary condition to determine the level of the exchange rates. It guarantees that prices are internationally equalized, which is a condition for purchasing power parities to hold. Under some additional assumptions, like fixed exchange rates, perfect commodity arbitrage implies international transmission of inflation (an increase in one price in domestic currency units is reflected in its counterpart in foreign currency units) and instantaneous effects on nominal prices of exchange rate adjustments. On the other side, a transitory absence of commodity price arbitrage can contribute to explaining shortrun volatility of exchange rates and "overshooting " effects. Following the usual definition, commodity arbitrage ensures that each good has a single price (defined in a common currency unit) throughout the world (Isard). This has been called the "Law of One Price" (LOP). Empirical studies on international prices frequently find significant and persistent deviations from equilibrium values either at the
Testing for the Cointegrating Rank of a VAR Process with a Time Trend
 DISCUSSION PAPER 51, SFB 373, HUMBOLDTUNIVERSITAT ZU
, 1997
"... Standard tests for the cointegrating rank of a vector autoregressive (VAR) process have nonstandard limiting distributions which depend on the characteristics of intercept terms and time trends in the system. In practice these characteristics are often unknown. Therefore modified tests are proposed ..."
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Cited by 80 (6 self)
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Standard tests for the cointegrating rank of a vector autoregressive (VAR) process have nonstandard limiting distributions which depend on the characteristics of intercept terms and time trends in the system. In practice these characteristics are often unknown. Therefore modified tests are proposed with limiting distributions which do not depend on the characteristics of deterministic terms under the null hypothesis. One type of tests makes use of lag augmentation, that is, a VAR process of order p + 1 is fitted when the true order is p while the tests are based on the coefficient matrices of the first p lags only. It is shown that Ø 2 limiting distributions are obtained in this way. The price for this simplicity will be reduced power, however. Therefore, we also consider LM (Lagrange multiplier) type tests. These tests are shown to have nonstandard limiting distributions which do not depend on deterministic terms and have better local power than competing LR (likelihood ratio) test...
Cointegration and LongHorizon Forecasting
 Journal of Business and Economic Statistics
, 1997
"... : We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate BoxJenkins forecasts are just as accurate. Our results ..."
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Cited by 46 (2 self)
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: We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate BoxJenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measuresthey fail to value the maintenance of cointegrating relationships among variables and we suggest alternatives that explicitly do so. KEY WORDS: Prediction, Loss Function, Integration, Unit Root  2  1. INTRODUCTION Cointegration implies restrictions on the lowfrequency dynamic behavior of multivariate time series. Thus, imposition of cointegrating restrictions has immediate implications for the behavior of longhorizon forecasts, and it is widely believed that imposition of cointegrating restrictions, when they are in fact true, will produce superior longhorizon forecasts. Stock (1995, p. 1), for ...
Some Further Evidence on the Law of One Price: The Law of One Price
 Still Holds, Amer0ican Journal of Agricultural Economics
, 1991
"... International trade models often postulate the existence of a representative price, i.e., the price which prevails at all markets. This is known as the "Law of One Price. " In this paper, the law of one price is tested for seven commodities among four countries by explicitly considering tr ..."
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Cited by 39 (2 self)
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International trade models often postulate the existence of a representative price, i.e., the price which prevails at all markets. This is known as the "Law of One Price. " In this paper, the law of one price is tested for seven commodities among four countries by explicitly considering transaction costs. The empirical evidence suggests that, in most cases, the law of one price cannot be rejected asa maintained hypothesis. Furthermore, for the remaining cases transaction costs seem to cause the failure. Key words: cointegration, "Law of One Price, " stationarity, transaction costs. International trade models of agricultural commodities often postulate the existence of a representative price, i.e., a price which prevails at all markets. This known as the "Law of One Pfice " (LOP). The LOP assumption is crucial, especially in empirical studies, because its violation may invalidate the studies ' conclusions. For example, a model of optimal intervention i a specific commodity market, domestic or international, requires a representative price. If an inappropriate price is dations based on such expected effects. This sistency of the LOP evidence. used, policy recommena model will not have the paper focuses on the conpostulate with empirical Traditionally, tests of the LOP have applied the following procedure: A commodity price in one country is regressed on the same commodity's price in another country. Then, the slope coefficient is restricted to equal one and (possibly) the intercept term is restricted to equal zero. If such restrictions are not rejected, the conclusion is that the LOP holds. However, such procedures have not yielded favorable results regarding the LOP (e.g., Isard and Richardson among others). Those tests have been criticized on several grounds. For example, CrouhyVeyrac, Crouhy, and Melitz cite the omission of transfer costs; if these costs were taken into
Understanding Spot and Forward Exchange Rate Regressions.” Journal of Applied Econometrics
 Evaluation of Extension and USDA Price and Production Forecasts. Journal of Agricultural and Resource Economics
"... Using the Kalman filter, we obtain maximum likelihood estimates of a permanent–transitory components model for log spot and forward dollar prices of the pound, the franc, and the yen. This simple parametric model is useful in understanding why the forward rate may be an unbiased predictor of the fut ..."
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Cited by 37 (3 self)
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Using the Kalman filter, we obtain maximum likelihood estimates of a permanent–transitory components model for log spot and forward dollar prices of the pound, the franc, and the yen. This simple parametric model is useful in understanding why the forward rate may be an unbiased predictor of the future spot rate even though an increase in the forward premium predicts a dollar appreciation. Our estimates of the expected excess return on shortterm dollardenominated assets are persistent and reasonable in magnitude. They also exhibit sign fluctuations and negative covariance with the estimated expected depreciation.